LETTERSPUBLISHED ONLINE: 24MAY 2009 | DOI: 10.1038/NGEO528

Structural reactivation in plate tectonicscontrolled by olivine crystal anisotropyAndréa Tommasi1*, Mickael Knoll1,2, Alain Vauchez1, Javier W. Signorelli3, Catherine Thoraval1

and Roland Logé2

Reactivation of structures inherited from previous collisionalor rifting events, especially lithospheric-scale faults, is amajor feature of plate tectonics. Its expression ranges fromcontinental break-up along ancient collisional belts1,2 to lineararrays of intraplate magmatism and seismicity3,4. Here we usemultiscale numerical models to show that this reactivationcan result from an anisotropic mechanical behaviour of thelithospheric mantle due to an inherited preferred orientation ofolivine crystals. We explicitly consider an evolving anisotropicviscosity controlled by the orientation of olivine crystals inthe mantle. We find that strain is localized in domains whereshear stresses on the inherited mantle fabric are high, and thatthis leads to shearing parallel to the inherited fabric. Duringrifting, structural reactivation induced by anisotropy resultsin oblique extension, followed by either normal extensionor failure. Our results suggest that anisotropic viscosity inthe lithospheric mantle controls the location and orientationof intraplate deformation zones that may evolve into newplate boundaries, and causes long-lived lithospheric-scalewrench faults, contributing to the toroidal component ofplate motions on Earth.

Texture-induced viscoplastic anisotropy is an intrinsic featureof crystalline materials deforming by dislocation creep. It entailsa directional dependence of the mechanical strength on thecrystal orientation. This behaviour, expressed macroscopically asan anisotropic viscosity, results from both the anisotropy of theelastic tensor and the discrete nature of dislocation glide alongdensely packed lattice directions on selected crystallographic planes.It depends on the crystal symmetry and, at the aggregate scale, onthe orientation of the constitutive crystals or texture. As they havefewer slip systems, low-symmetry minerals are more anisotropicthan cubic metals. Orthorhombic olivine is highly anisotropic: ithas only three independent slip systems. At high temperature, anolivine crystal deforms up to 100 times faster if it activates the‘easy’ (010)[100] system rather than the ‘hard’ (010)[001] system5,6.This leads to development of strong crystal preferred orientations(texture), which are ubiquitous in naturally and experimentallydeformed mantle rocks7. Moreover, seismic anisotropy providesevidence for coherent orientation of olivine crystals at the scale ofhundreds of kilometres in the upper mantle8. Yet, in contrast tothe large number of studies on the role of texture-induced plasticanisotropy on the deformation of cubic and hexagonal metallicalloys since the early work of ref. 9, plastic anisotropy has beenlargely ignored in earth sciences.

Models considering a transversely isotropic viscosity showednevertheless that anisotropy changes the convection length scales,

1Geosciences Montpellier, CNRS & Université de Montpellier 2, Pl. E Bataillon, 34095 Montpellier cedex 5, France, 2MINES ParisTech, CEMEF—Center forMaterials Forming, UMR CNRS 7635, BP207, 06904 Sophia Antipolis Cedex, France, 3Instituto de Fisica de Rosario, CONICET, Universidad Nacional deRosario, 2000 Rosario, Argentina. *e-mail: andrea.tommasi@gm.univ-montp2.fr.

leads to strain localization, and modifies the initiation times ofconvective instabilities in the mantle10–12. Mechanical anisotropydue to olivine crystal preferred orientations in the mantle wasalso proposed to explain the reactivation of ancient collisionalstructures during continental rifting2. Models of the deformation ofa homogeneous, anisotropic mantle subjected to an axisymmetrictension show a strong directional softening, leading to strainlocalization and development of shearing when extensional stressesare oblique to the pre-existing mantle fabric13. These modelsavoided simplifications to the viscosity tensor by using a viscoplasticself-consistent (VPSC) formalism14 to relate the crystal and large-scale plastic anisotropies, but they did not allow for the evolutionof olivine textures and, hence, of the anisotropy in response tothe new solicitation.

To fully account for an evolving anisotropic viscosity as afunction of the orientation of olivine crystals in the mantle, wecoupled the VPSC formalism to FORGE2005, a commercializedthree-dimensional finite-element mechanical (FEM) code. Thecoupling is performed through a set of 1,000 olivine crystalsassociatedwith each finite element. After each FEM time increment,the local velocity gradient tensor is used as a boundary conditionfor the VPSC simulation, leading to evolution of the polycrystaltexture and viscosity. The updated polycrystal viscosity tensor isthen used to calculate the stress field in the next FEM time step (seeSupplementary Fig. S1).

To analyse the deformation of a plate containing a pre-existinglithospheric-scale transcurrent shear zone or transpressional belt,we run a series of models using a plate with aspect ratio 1.2×1×0.1(Fig. 1) subjected to a constant divergent velocity or tensionalstress on its left lateral boundary. Free-slip conditions (normalvelocities and shear stresses are null) are imposed on the oppositeboundary. Boundaries normal to the y and z axes are free (normaland tangential stresses are null). We use a multidomain meshingtool to define a planar zone, 0.1 or 0.2 units wide, cross-cuttingthe entire plate, at 45◦ (Fig. 1) or normal to the x axis (seeSupplementary Fig. S2). This zone has an initial ‘wrench-fault-type’olivine texture15; maximum concentrations of [100] and [010] axesare horizontal, respectively parallel and normal to the shear-zonetrend (Fig. 1). This texture is coherent with shear-wave splittingdata in large-scale strike-slip faults and transform boundaries,where fast S waves are polarized parallel to the trend of the faultup to 50 km away from the surface expression of the fault16,and in collisional belts8,15,17. For numerical stability reasons, theinitial texture is however significantly weaker (Jindex = 3, Fig. 1,where Jindex is a measure of the texture intensity, expressed as thevolume-averaged integral of the squared orientation densities) than

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO528

Final texture

Initial texture

Olivine crystalslip systems

¬0.005

Shear strain εxy

¬0.025

x

x'

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z

3.44 3.10 1.67

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[100]

[010]

[010]

[001]

[001]

[100] [010] [001]

9.4 4.6 2.3

x

y

x

y

ε

Figure 1 |Geometry, boundary conditions and shear-strain εxy distribution in a model with an ’inherited shear zone’ at 45◦ of the imposed extensiondirection after a total stretching of 40%. Texture-induced anisotropy results in strain localization and higher shear strain in the ’inherited shear zone’.Evolution of the olivine texture within the ’inherited shear zone’ may be evaluated by comparing the initial (top left) and final (bottom right) textures.Bottom left: slip systems in the olivine crystal, ’easy’ (010)[100] and (001)[100] systems are outlined by dark-grey shading and thicker lines parallel to theslip direction.

¬0.6

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in ra

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om)

a b

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om)

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0.10 0.2 0.3 0.4 0.5Imposed extension

0.10 0.2 0.3 0.4 0.5Imposed extension

45° shear zone

ε.eqε.x’y’

ε.y’y’ε.zzεεεε

External domain

ε.eqε.xy

ε.xxε.zz

εεε

εExternal domain

ε.eqε.xy

ε.xxε.zz

εεε

ε90° shear zone

ε.eqε.x’y’

ε.y’y’ε.zz

ε εεε

Figure 2 | Evolution of strain rates in the inherited texture zone (thick lines) and in the surroundings (thin lines) as a function of the imposedextension. a, Inherited ‘shear zone’ at 45◦ to the imposed extension. b Inherited ‘shear zone’ normal to the imposed extension. Analysis of the Von Misesequivalent strain rate ε̇eq=

√2/3ε̇ijε̇ij highlights the evolution of the strain distribution in response to the reorientation of the olivine crystal preferred

orientations in both domains. The latter also results in changes in the deformation regime, outlined by the evolution of the rates of shearing parallel to theinherited shear zone (ε̇x′y′ ), extension normal to it (ε̇y′y′ ) and vertical thinning (ε̇zz).

those from naturally deformed peridotites7 (2< Jindex< 26, peak at8).Olivine texture in the surroundingmedium is initially random.

All models show an anisotropic behaviour, characterized bydependence of strength on the direction of solicitation relative tothe texture orientation. Strain localization arises owing to lateralvariations in texture orientation and intensity. Equivalent strainrates (ε̇eq) are higher when the texture orientation relative to theimposed extension results in high resolved shear stresses on the‘easy’ (010)[100] and (001)[100] slip systems inmost crystals withina domain. Strain is therefore localized in the ‘inherited texturedomain’ at 45◦ to the imposed extension (Figs 1 and 2a), whereas asimilar domain normal to the extension has a higher initial strength,deformingmore slowly than the surroundingmedium (Fig. 2b).

Decomposition of the horizontal flow field into its poloidal(divergence) and toroidal (vorticity) components highlights thatviscoplastic anisotropy produces lateral variations in the poloidalflow field (strain localization) and toroidal flow (strike-slipdeformation) in the ‘inherited texture domain’ (Fig. 3). The latterdeforms therefore by transtension (Fig. 2): shearing parallel to itstrend (ε̇x ′y ′) accompanies stretching normal to it (ε̇y ′y ′) and verticalthinning (ε̇zz). The intensity of the toroidal component dependsto the first order on the orientation of the texture relative to thestress field, but also on the texture intensity. It is higher in ‘inheritedtexture domains’ oblique to the extension direction and for strongerinitial textures (see Supplementary Fig. S3). Analysis of the resultsof the model with an ‘inherited texture domain’ normal to the

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NATURE GEOSCIENCE DOI: 10.1038/NGEO528 LETTERS

1.8 1.9 2.0 2.1 2.2 2.3 ¬0.8 ¬0.6 ¬0.4 ¬0.2 0 0.2

Divergence (µ104) Vertical vorticity (µ104)

Divergence (µ104) Vertical vorticity (µ104)2.05 2.10 2.15 2.20 2.25 2.30 ¬0.8 ¬0.6 ¬0.4 ¬0.2 0 0.2

a

c

b

d

Figure 3 | Poloidal–toroidal partitioning in the models. Maps of the divergence (a,c) and vorticity (b,d) of the horizontal flow field. Higher divergencevalues indicate strain localization in the ‘inherited texture domain’ or in the surroundings, when the former is at 45◦ (a) or normal (b) to the imposedextension. Larger divergence variations denote stronger localization in the 45◦ model. Toroidal flow, indicated by a non-null vorticity, is restricted to the‘inherited texture domain’. Divergence and vorticity variations are directly related to changes in the olivine texture, being roughly homogeneous withineach domain.

extension shows however that even a slight departure from perfectsymmetry of the texture (see Supplementary Fig. S2) producestoroidal flow (Fig. 3) and hence horizontal shearing within theinherited texture domain (Fig. 2b).

Evolution of olivine textures with increasing strain modifiesthe strain distribution. Progressive rotation of olivine [100] and[010] axes towards the maximum finite extension and shorteningdirections, respectively (Fig. 1), results in geometrical hardening inboth the ‘inherited texture domain’ and the surroundings (Fig. 2),because shear stresses on the ‘weak’ (010)[100] and (001)[100]slip systems decrease. Faster texture evolution in the ‘inheritedtexture domain’ in the 45◦ model (the surroundings in the 90◦ one)results in rehomogenization of the strain distribution (inversion ofthe strength contrast) at high strain. Texture evolution and hencethe mechanical behaviour depend on the strain regime: extensionor compression normal to the dominant orientation of the easyslip systems produce hardening, whereas shearing parallel to itproduces softening (see Supplementary Fig. S4). Reorientation ofthe olivine texture also changes the deformation regime in the‘inherited texture domain’ (Fig. 2). In the 45◦ model, the shearrate parallel to the trend of the ‘inherited texture domain’ (ε̇x ′y ′)decreases and the extension rate normal to it (ε̇y ′y ′) increases; thedeformation evolves from transtensional to extensional (Fig. 2a).

Although extremely simple (they do not consider thermal effectsand test only end-member geometries), these models show that

viscoplastic anisotropy due to preferred orientation of olivinecrystals triggers the reactivation of pre-existing lithospheric-scalefaults or transpressional belts if their orientation enables highershear stresses on the olivine crystals’ easy slip systems within themthan in the surroundings. Strain localization in the presentmodels islimited: the strain-rate contrast between the domain with inheritedtexture and the initially isotropic surroundings is less than 2 (Fig. 2).This contrast is enhanced if the inherited texture is stronger,like those usually observed in naturally deformed peridotites (seeSupplementary Fig. S3), or if the surroundings have a non-randominitial texture in a ‘hard’ orientation relatively to the solicitation,but texture-induced mechanical anisotropy remains less effectivein producing strain localization than changes in deformationmechanism due to grain refinement18, viscous heating19 or damageprocesses20. However, the latter are observed neither in high-temperature, high-pressure experiments nor in nature and theformer processes require an already localized forcing, that is, apre-existing localization of the deformation21, usually produced ingeodynamical models by the introduction of ad hoc temperatureanomalies or ‘weak domains’. Viscoplastic anisotropy due tocoherent orientation of olivine crystals, in contrast, is an intrinsicfeature of lithospheric plates as shownby shear-wave splitting8.

We propose that lateral variations in mechanical behaviour dueto changes in the inherited olivine crystal preferred orientationswithin a plate represent a major ‘seed’ process for strain localization

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LETTERS NATURE GEOSCIENCE DOI: 10.1038/NGEO528

creating the conditions for the activation of additional efficientlocalizing processes. In contrast to lateral variations of thegeotherm, crustal thickness, or damage zones associated with brittlefaults that may also seed localization, its lifetime is not limitedby heat diffusion, isostatic re-equilibration, or erosion. Coherencebetween crustal structures of all ages and seismic anisotropy datasuggest that texture-induced anisotropy may be preserved for morethan 1Gyr. It may therefore explain the reactivation of lithospheric-scale strike-slip or transpressional zones hundreds of Myr old, asobserved in the South Atlantic and East African rifting2,13.

Deformation controlled by texture-induced viscoplasticanisotropy associated with lithospheric-scale wrench faults andtranspressional belts has a characteristic signature: developmentof shearing parallel to the trend of the reactivated structures.Rift initiation controlled by anisotropy-induced reactivation ofshear zones results in transtension followed by normal extension.This evolution is observed in the East African rift22, the NorthAtlantic margins23, the Rhine graben24 and the eastern Gondwanabreak-up25. It supports reactivation of neoproterozoic belts duringthe easternGondwana and East African rifting, of Caledonian struc-tures in the North Atlantic opening and of Variscan wrench faultsin the Rhine graben. It also suggests that the role of mechanicalanisotropy decreases in mature rift systems, in agreement with thepresent models’ prediction that evolution of the olivine textureleads to progressive geometric hardening and, hence, to rift failure,if thermo-mechanical or magmatic processes leading to furthersoftening are not activated in the thinned lithospheric domain.

As it favours shearing parallel to the pre-existing mantlestructure, viscoplastic anisotropy may also explain the reactivationof large-scale wrench faults during successive collisional andextensional episodes, such as the Newfoundland–Azores–Gibraltarfault zone, which acted as a dextral strike-slip boundary duringthe Hercynian orogeny26 and was reactivated as a major transformaccommodating the differential motion between Africa and Europeduring the Central Atlantic opening. The large proportion ofstrike-slip focal mechanisms in intraplate seismic arrays, such asthe New Madrid seismic zone in the southeastern US (ref. 27) orthe present seismic activity along the Hercynian South Armoricanshear zone in France28, also suggests that the reactivation of theNE–SW- andNW–SE-trendingmantle fabric imaged by shear-wavesplitting in the southeasternUS (ref. 29) andBrittany30 probably hasa significant role in this intraplate deformation process.

A major consequence of viscoplastic anisotropy is that thestress and strain tensor eigenvectors are parallel only when theolivine texture is perfectly symmetric relatively to the stressfield. Even a slight departure from symmetry produces shearingparallel to the average orientation of the dominant olivine slipsystem. Reactivation of a strike-slip or transpressional mantletexture therefore produces toroidal flow. The toroidal–poloidalpartitioning depends on the orientation of the texture relativeto the solicitation. In the present models (Fig. 3), the ratiobetween the vorticity and the divergence of the horizontal velocityfield ranges from 0.2 to 0.3 (0.7 for a stronger initial olivinetexture, Supplementary Fig. S3). These values encompass theaverage toroidal–poloidal partitioning ratio in the Earth (0.3–0.4;ref. 31), suggesting that texture-induced viscoplastic anisotropyin the mantle may significantly contribute to the Earth mantletoroidal flow and to belt-parallel transport recorded by both strainpartitioning in the crust and fast-shear-wave polarization in pastand present convergent boundaries17.

MethodsA VPSC formalism14 is used to relate the crystal and polycrystal mechanicalbehaviours and to predict the texture evolution. Interaction between the crystal andthe polycrystal is calculated using the Eshelby formalism; each crystal is consideredas an inclusion embedded in a homogeneous equivalent medium that behavesas the average of all crystals. At the crystal scale, deformation is accommodated

by dislocation glide on discrete slip systems, whose relative strength—or criticalresolved shear stress—depends on the temperature, pressure and chemicalenvironment. In the present simulations, critical resolved shear stresses (τ0)and stress exponents (n) derived from high-temperature experiments on dryolivine crystals5,6 were used: τ [100](010)0 = τ

[100](001)0 = 1/2τ [001](010)0 = 1/3τ [001](100)0

and n= 3 for all systems. Two additional slip systems, which are not observed inolivine, {1̄11}〈110〉 and {111}〈110〉, with τ0 = 50∗τ [100](010)0 , are added to ensureconvergence. They never accommodatemore than 1%of the total strain.

Three-dimensional FEM modelling. FORGE2005 is a commercialized FEMsoftware using an updated Lagrangian scheme. The finite-element formulationis based on a mixed velocity–pressure formulation with an enhanced (P1+/P1)four-node tetrahedral element. Thermal effects are not considered. The mesh usedin the present simulations is composed of about 12,000 linear tetrahedral elements.To define regions showing different initial textures, we use a multidomain meshtool based on a level-set function32. Heterogeneous mesh refinement allows a finedescription of the interfaces with aminimumnumber of mesh elements. Resolutiontests using about 9,000, 12,000, and 25,000 linear elements corroborate that strainlocalization does not depend on the mesh; the strain rate is roughly constant withineach domain (small variations are observed close to the free boundaries) and theratio between the average equivalent strain rates in the inherited texture domainand in the surroundings are similar. Low-resolution tests with about 4,500 elementsshow in contrast significantly weaker strain localization. To enable comparisonbetween models, strain rates are normalized by the initial Von Mises equivalentstrain rate, ε̇eq =

√2/3ε̇ij ε̇ij , of the surrounding medium, which has an initially

random texture and hence an isotropic behaviour.

Received 4 February 2009; accepted 24 April 2009;published online 24 May 2009

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AcknowledgementsThis study was partially funded by the programme Action Marges of the Institut Nationaldes Sciences de l’Univers, Centre National de la Recherche Scientifique (INSU-CNRS),France. Collaboration with J.S. was supported by a CNRS-CONICET cooperationprogram. M.K. benefited from a PhD scholarship from the Ministère de la Recherche etde l’Enseignement Supérieur, France.

Author contributionsThis work is the outcome of a study on the effect of olivine fabrics on the mechanicalbehaviour of the continental lithosphere started by A.V. and A.T. M.K. ran all simulationsas part of his Ph.D. under the supervision of A.T. and R.L. J.W.S. performed thecoupling between the VPSC and the FEM codes. C.T. assisted in the analysis ofthe modelled flow fields.

Additional informationSupplementary information accompanies this paper on www.nature.com/naturegeoscience.Reprints and permissions information is available online at http://npg.nature.com/reprintsandpermissions. Correspondence and requests for materials should beaddressed to A.T.

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